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2020

2020 Math Kangaroo Grades 5-6 past paper

Suitable for 5-6 Grade, 30 MC questions.

Sample ProblemsDownload PDF
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30 Questions
75 Minutes
3/4/5 Tiered Scoring
No Calculator
Exam Overview

Exam Overview

Number TheoryLogic proportionstablecertain, Geometry.

DDifficulty

  • 3 pointsQ 1-10
  • 4 pointsQ 11-20
  • 5 pointsQ 21-30

TTopics

  • Fraction Operations25%
  • Geometry25%
  • Number Theory20%
  • Combinatorics15%
  • Logic15%

AAwards

Super Gold
Top 1%
90+
Gold
Top 5%
80+
Silver
Top 15%
65+
Bronze
Top 30%
50+
Sample Problems

2020 Kangaroo Level E Sample Problems (8 questions)

Selected problems across difficulty tiers — click an option to check your answer

Q 3Easy 3 pointsCounting
Choose 3 balls from 10 distinct balls. How many ways?
A) 120
B) 720
C) 210

Steps

1C(10,3)=10x9x8/(3x2x1)=120
Answer: ACombination
Q 8Easy 3 pointsSequence
10th term of 3,7,11,...?
A) 39
B) 43
C) 47

Steps

1a10=a1+9d=3+9x4=39
Answer: AArithmetic sequence
Q 12Medium 4 pointsGeometry
Triangle sides 5,12,13. Inradius?
A) 2
B) 3
C) 6

Steps

1Right triangle, area=30, semiperimeter=15, r=area/s=2
Answer: AIncircle
Q 16Medium 4 pointsCombinatorics
4 people shake hands once each. Total handshakes?
A) 6
B) 12
C) 24

Steps

1C(4,2)=6
Answer: ACombination
Q 21Hard 5 pointsNumber Theory
gcd(48,36) x lcm(48,36) = ?
A) 48x36
B) 1728
C) 432

Steps

1gcd x lcm = product = 48x36
Answer: Agcd and lcm
Q 25Hard 5 pointsProbability
Flip 3 coins. Probability all heads?
A) 1/8
B) 1/4
C) 3/8

Steps

1(1/2)^3=1/8
Answer: AIndependent events
Q 28Hard 5 pointsNumber Theory
How many multiples of 3 from 1 to 100?
A) 33
B) 34
C) 30

Steps

1⌊100/3⌋=33
Answer: ADivisibility
Q 30Hard 5 pointsCombinatorics
How many 3-digit numbers with distinct digits from 1,2,3,4?
A) 24
B) 12
C) 64

Steps

14x3x2=24
Answer: APermutation

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